| James Robert Christie - Mathematics - 1866 - 404 pages
...described about a circle are together equal to the other two opposite sides. 5. If two triangles have **one angle of the one equal to one angle of the other,** and the sides about the equal angles proportionals, the triangles shall be equiangular, and &c. 6.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham **one angle of the one equal to one angle of the other, have** to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...GFL, and BA is to AE as GFis to FL. [VI. Definition I. And, because the triangles ABE and FGL have **one angle of the one equal to one angle of the other,** and the side* about these equal angles proportionals, therefore the triangle ABE is equiangular to... | |
| Edinburgh univ - 1868
...the segments of the other. 4. To inscribe a circle in a given triangle. 5- Equal triangles which have **one angle of the one equal to one angle of the other, have their sides about the equal angles** reciprocally proportional. 6. Find the continued product of (x + y + z), ( - x + y + z), (x - y +«),... | |
| Elizabethan club - 1880
...the line which meets it, the line which meets shall touch the circle. 49 10. If two triangles have **one angle of the one equal to one angle of the other,** and the sides about the equal angles proportionals, the triangles shall be equiangular to each other,... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880
...the hexagon, prove that the square on AC is three times the square on AB. 10. If two triangles have **one angle of the one equal to one angle of the other,** and the sides about the equal angles proportionals, the triangles are similar. If two chords AB, AC... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...the triangle DEF. Wherefore, if two triangles &c. QED PROPOSITION 7. THEOREM. If two triangles have **one. angle of the one equal to one angle of the other,** and the sides about two other angles proportionals; then, if each of the remaining angles be either... | |
| Simon Newcomb - Geometry - 1881 - 399 pages
...Angle A — angle FMN = angle D; ) ,„. Angle B = angle FMN = angle E. \ ^ ' QED THEOREM VII. 393. Two **triangles having one angle of the one equal to one angle of the other,** and the sides containing these angles proportional, are similar. Hypothesis. ABC and A'B'C', two triangles... | |
| Education, Higher - 1884
...homologous sides shall either be equal, or be together equal to two right angles. 15. Triangles which have **one angle of the one equal to one angle of the other, have** to one another the ratio which is compounded of the ratios of their sides. Algebra. Junior, Senior,... | |
| |